More particularly, the invention pertains to a computer method for estimating a suite of quantities associated with locations of a space, for example a method for modeling petrophysical quantities of a reservoir or a method for mapping the depth or thickness of a geological layer.
In the area of oil exploration, it is sought to obtain information about subsurfaces, so as to be able to predict the presence of hydrocarbons to be extracted. Regular recourse is had to observation methods for estimating the quantities associated with certain locations of the space. To reduce to the maximum the recourse to these observation methods, which are expensive to implement, the computing tool is used to estimate the quantities at locations where no measurement has been performed.
In particular, use is made of interpolation methods such as kriging. Kriging is an unbiased interpolator which minimizes the mean square prediction error and which makes it possible to honor the available data (it is an exact interpolator).
An example of such a method is for example described in U.S. Pat. No. 7,254,091.
A difficulty related to kriging is that it requires large computational power to invert the covariance matrix. This is true in particular when working on a large space, using numerous observation data.
To alleviate this problem, in the case of large suites of observation data, it is possible as a variant to work on sub-spaces. For each point studied for which it is sought to estimate the quantity, local reasoning is employed by searching for the observation data obtained for the points nearest to the point studied, and by using a local covariance matrix reduced to these points. The computation time necessary for the inversion of a large matrix is then reduced by implementing a nearest neighbors search and the inversion of a smaller matrix. This search and this inversion must however be repeated for each point to be estimated. To reduce to the maximum the computation times, there is then a tendency to limit as much as possible the number of observations to be taken into account (i.e. the number of neighbors), so as to limit as much as possible the size of the matrices to be inverted.
This method is problematic however. On the one hand, it is very sensitive to the spatial distribution of the observation data, this sensitivity is manifested by neighborhood artifacts. Moreover, it may still be greedy in terms of computation time in the search for the neighborhoods.